Difference between revisions of "Conservation of Angular Momentum"
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| − | '''Conservation of angular momentum''', fundamental concept of physics along with the conversations of mass and energy as well as [[momentum (physics)|linear momentum]]. It further states that the amount of angular momentum remains constant unless changed through an action of external forces as described by [[Isaac Newton|Newton's]] [laws of motion]. | + | '''Conservation of angular momentum''', fundamental concept of physics along with the conversations of mass and energy as well as [[momentum (physics)|linear momentum]], and defined as mass multiplied by velocity of an object. It further states that the amount of angular momentum remains constant unless changed through an action of external forces as described by [[Isaac Newton|Newton's]] [laws of motion]. |
The angular momentum of a point mass about a point is defined as <math>\vec H = \vec r \times \vec p</math> where <math>\vec{r}</math> is the position [[vector quantity|vector]] of the point mass with respect to the point of reference and <math>\vec{p}</math> is the [[momentum (physics)|linear momentum]] vector of the point mass. | The angular momentum of a point mass about a point is defined as <math>\vec H = \vec r \times \vec p</math> where <math>\vec{r}</math> is the position [[vector quantity|vector]] of the point mass with respect to the point of reference and <math>\vec{p}</math> is the [[momentum (physics)|linear momentum]] vector of the point mass. | ||
Revision as of 20:28, October 1, 2016
Conservation of angular momentum, fundamental concept of physics along with the conversations of mass and energy as well as linear momentum, and defined as mass multiplied by velocity of an object. It further states that the amount of angular momentum remains constant unless changed through an action of external forces as described by Newton's [laws of motion].
The angular momentum of a point mass about a point is defined as 
where 
is the position vector of the point mass with respect to the point of reference and 
is the linear momentum vector of the point mass.
The principle of angular momentum can be applied to a system of particles by summing the angular momentum of each particle about the same point. This can be represented as:
where
is the total angular momentum of the system
is the angular momentum of the ith particle
The derivative of angular momentum with respect to time is equal to the sum of the external moments (or torque 
) applied to the system. Differentiating angular momentum gives:
For a constant radius, the second term is zero. Hence 
From this, it can be concluded that in the absence of an external moment, angular momentum must be conserved.
